Some PHP help please

When somebody visits my bbpress forum http://storeeboard.com , they are presented with the login form at the top of the page. Once they login, the form disappears and what appears is the ‘Welcome, *username* | Logout’ information.

My question is, how do I get other text on the page to ‘disappear’ once somebody has logged in.

I have a ‘Sign Up’ link on the page that I would like to disappear once a user logs in.

My php skills aren’t all that great but I know my way around xhtml and css.